Surfaces generated by moving least squares methods
Authors:
P. Lancaster and K. Salkauskas
Journal:
Math. Comp. 37 (1981), 141158
MSC:
Primary 65D05; Secondary 41A05, 41A63
MathSciNet review:
616367
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Abstract: An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analysis is accompanied by examples of univariate and bivariate problems.
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 [1]
 R. E. Barnhill, Representation and Approximation of Surfaces, Mathematical Software III, Academic Press, New York, 1977, pp. 69120. MR 0489081 (58:8556)
 [2]
 R. W. Clough & J. L. Tocher, "Finite element stiffness matrices for analysis of plates in bending," in Proc. Conf. Matrix Methods in Structural Mechanics, WrightPatterson A.F.B., Ohio, 1965.
 [3]
 R. Franke & G. Nielson, Smooth Interpolation of Large Sets of Scattered Data, Technical Report #NPS5379005, Naval Postgraduate School, Monterey, Calif., 1979. MR 593596 (82d:65011)
 [4]
 W. J. Gordon & J. A. Wixom, "Shepard's method of 'metric interpolation' to bivariate and multivariate data," Math. Comp., v. 32, 1978, pp. 253264. MR 0458027 (56:16230)
 [5]
 P. Lancaster, "Moving weighted leastsquares methods," in Polynomial and Spline Approximation (B. N. Sahney, Ed.), NATO Advanced Study Institute Series C, Reidel, Dordrecht, 1979, pp. 103120. MR 545641 (80c:65037)
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 P. Lancaster, "Composite methods for generating surfaces," in Polynomial and Spline Approximation (B. N. Sahney, Ed.), NATO Advanced Study Institute Series C, Riedel, Dordrecht, 1979, pp. 91102. MR 545640 (81c:41075)
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 D. H. Mclain, "Drawing contours from arbitrary data points," Comput. J., v. 17, 1974, pp. 318324.
 [8]
 L. Mansfield, "Higher order compatible triangular finite elements," Numer. Math., v. 22, 1974, pp. 8997. MR 0351040 (50:3531)
 [9]
 M. J. D. Powell & M. A. Sabin, "Piecewise quadratic approximation on triangles," ACM Trans. Math. Software, v. 3, 1977, pp. 316325. MR 0483304 (58:3319)
 [10]
 S. Ritchie, Representation of Surfaces by Finite Elements, M.Sc. Thesis, University of Calgary, 1978.
 [11]
 D. Shepard, A TwoDimensional Interpolation Function for Irregularly Spaced Points, Proc. 1968 A.C.M. Nat. Conf., pp. 517524.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106163671
PII:
S 00255718(1981)06163671
Article copyright:
© Copyright 1981
American Mathematical Society
